In the perfect eye, an incoming beam of light is focused through the cornea and through the crystalline lens in a way which causes all of the light from a point source to converge at the same spot on the retina of the eye. This convergence occurs because all of the optical path lengths, for all light in the beam, are equal to each other. Stated differently, in the perfect eye, the time for all light to transit through the eye will be the same regardless of the particular path that is taken by the light.
Not all eyes, however, are perfect. The consequences of this are that light path lengths through the eye become distorted and are not all equal to each other. Thus, light from a point source that transits an imperfect eye will not necessarily be focused on the retina, or to the same spot on the retina.
As light enters and passes through an eye it is refracted at the anterior surface of the cornea, at the posterior surface of the cornea, and at the surfaces of the crystalline lens. It is after all of these refractions have occurred that the light finally reaches the retina. As indicated above, in the case of the perfect eye, all of these refractions result in no overall change in the optical path lengths of light in the incoming beam. Therefore, any deviations which result in unequal changes in these optical path lengths are indicative of imperfections in the eye which may need to be corrected.
In general, vision difficulties in the human eye can be characterized by the changes and differences in optical path lengths that occur as light transits through the eye. These difficulties are not uncommon. Indeed, nearly one half of the world's population suffers from imperfect visual perception. For example, many people are near-sighted because their eyeballs are "too long" (myopia). As a result, the sharp image of an object is generated not on the retina, but in front of or before the retina. Therefore, for a myopic person a distant scene appears to be more or less blurred. On the other hand, hyperopia is a condition wherein the error of refraction causes rays of light entering the eye parallel to the optic axis to be brought to a focus behind the retina. This happens because the eyeball is "too short" from front to back. This condition is commonly referred to as far-sightedness. Unlike the myopic person, a hyperopic, or far-sighted, person will see a near scene as being more or less blurred.
Another refractive malady is astigmatism. Astigmatism, however, is different than either myopia or hyperopia in that it results from an unequal curvature of the refractive surfaces of the eye. With astigmatism, a ray of light is not sharply focused on the retina but is spread over a more or less diffuse area. Further, there are even higher order refractive maladies of interest for vision correction which include coma and spherical aberration. More specifically, coma is an aberration in a lens or lens system whereby an off-axis point object is imaged as a small pear-shaped blob. Coma is caused when the power of the zones of the lens varies with distance of the zone from the axis. Spherical aberration, on the other hand, results from loss of definition of images that are formed by optical systems, such as an eye. Such aberrations arise from the geometry of a spherical surface.
In the past, simple refractive errors of the human eye (myopia, hyperopia and astigmatism) have been corrected conventionally with glasses, dating back to the year 1750. More recently, contact lenses, which were invented about 50 years ago, have been useful for correcting these same more simple refractive errors. Further, refractive laser surgery using Excimer UV-lasers is receiving increased popularity. Thus far, however, all of these techniques for correcting optical impairments of the eye have been limited to the correction of errors from near-sightedness (myopia) or far-sightedness (hyperopia), and to the cylindrical refractive errors, the so-called astigmatism.
As noted above, vision and its refractive errors can be quite complex. Similar to every other optical system, in addition to the simple refractive errors, the human eye also shows higher order refractive errors ("aberrations") such as coma and spherical aberration mentioned above. In all cases, aberrations result when an ideally flat `wavefront` (i.e. a condition wherein all optical path lengths are equal) is distorted by a real-world optical system. In some cases, these distortions occur in a very complex way. In the trivial case, simple distortions like nearsightedness and far-sightedness would result in an uncomplicated bowl-like symmetrical distortion. With higher order aberrations, however, the result is a complex non-symmetrical distortion of the originally flat wavefront. It is these non-symmetrical distortions which are unique for every optical system, including every single person's eye, and which lead to blurred optical imaging of viewed scenes.
It happens that refractive errors (aberrations or distortions) are stronger when light not only passes through the center of an optical system, but also through the outer regions of the system. Specifically, these aberrations are more pronounced under critical lighting conditions (e.g., twilight). For example, it is well known that people have a comparably small pupil in bright daylight. As the light level decreases, however, the pupil becomes dilated in order to let more light pass through to the retina. With dilation, in addition to passing through the center of the eye light rays will also pass through the outer region of the eye (e.g. the optical system), where the optical quality is low. Thus, even persons with normal 20/20 vision have decreased visual acuity under critical light conditions due to increased higher order aberrations.
A typical approach for improving the vision of a patient has been to first obtain measurements of the eye which relate to the topography of the anterior surface of the cornea. Specifically, such measurements are made to determine the Zernike polynomials. The Zernike polynomials are then used to mathematically describe and to model the anterior surface of the cornea. In accordance with this practice, depending on the order of the Zernike polynomial a certain refractive condition of the eye can be described. For example, the first order terms of the Zernike polynomials describe the tilt of a wavefront while second order terms describe myopia, hyperopia and astigmatism. Third order terms then describe coma and fourth order terms describe i.e. spherical aberration.
Until now, the complex aberrations of the human eye involving coma and spherical aberration could not be measured and, therefore, they could not be corrected. Further, even today, the measurement of the `standard` so-called simple refractive errors is still not fully objective. In fact, presently the patient's vision is usually categorized using an autorefractor for measuring near-sightedness, far-sightedness, and astigmatism. In the process, cooperation of the patient is crucial for obtaining even rough realistic results with these systems. Still, after this rough initial measurement, the optometrist has to use correction lenses in a subjective procedure to find the corrective strength that is best suited for the patient. To a great extent, these limitations have been caused by an inability to determine a topography for the posterior surface of the eye in addition to determining the topography of the anterior surface. Further, there has been little attention given to the peripheral areas of the cornea where spherical aberrations become more prominent as the pupil of the eye dilates. In order to overcome these deficiencies, it is necessary to evaluate new ways and methods for measuring the refractive characteristics of the cornea.
Heretofore, it has been a common practice to analyze and describe light beams in terms of wavefronts and aberrations of a wavefront. In this regard, the Zernike polynomials have been helpful. A light beam, however, can be conceptualized in a different way; other than as a wavefront. It can also be thought of in terms of a plurality of individual beams, each of which has its own optical path length. Specifically, by way of comparison, at any particular point in time a wavefront can be thought of as being the temporal lengths of the various optical paths that have been traveled by individual light beams from the origin or source of the light. Thus, a light beam with a flat or planar wavefront is equivalent to a light beam wherein all light in the beam has traveled on optical paths that have the same temporal length. A wavefront can be distorted by imperfections in the eye and result in so-called wave aberrations. In terms of optical path lengths, these same aberrations can be thought of as resulting from differences in the optical path lengths of individual beams which are caused by undesirable refractions of light as it passes through the eye.
As discussed above, until now vision correction has been primarily concerned with reshaping the cornea using data that is collected about the topography of the anterior surface of the eye. A good example of technology that is useful for this purpose is provided in U.S. Pat. No. 5,062,702 which issued to Bille for an invention entitled "Device for Mapping Corneal Topography." The posterior surface of the eye, however, also affects the refraction of light as it passes through the eye. Thus, additional information about the thickness of the cornea is necessary for more precise refractive corrections. To this end, a map of the posterior surface of the cornea would undoubtedly be useful. Further, while gross approximations of the lower order visual aberrations using the Zernike polynomials may be useful for limited purposes, the superficial models provided by the Zernike polynomials become quite cumbersome and less precise when higher order aberrations are concerned.
In light of the above, it is an object of the present invention to provide a method and apparatus for measuring the refractive properties of the human eye that are capable of creating a topographical map of the anterior surface of the eye and an acuity map of the refractive power of the entire human eye which are useful either for the prescription of corrective elements or to plan for surgery. Another object of the present invention is to provide a method and apparatus for measuring the refractive properties of the human eye by considering the net effect on individual beams as they each pass through the eye. Yet another object of the present invention is to provide a method and apparatus for measuring the refractive properties of the human eye which, in addition to myopia, hyperopia and astigmatism, can also be used to determine higher order refractive error (aberrations) such as coma and spherical aberration. Still another object of the present invention is to provide a method and apparatus for measuring the refractive properties of the human eye which are effectively easy to use, relatively simple to operate and implement, and comparatively cost effective.